For Fallout 3, I'd have to say the Infiltrator. It was great.

For New Vegas, I'd say AMR or Survivalist Rifle.

For Fallout 4? I can't pick. They all suck. Unless I can choose modded guns.

Fallout 3: Xuanlong Assault Rifle

Fallout New Vegas: AER-14 Prototype (EVE Version)

Fallout 4: Splattercannon

Fallout 2:Bozar
Fallout 3: Lincolns rifle
Fallout new vegas:Anti-material sniper rifle
Fallout 4:Auto plasma rifle

Fallout 1 alien blaster... Something about stumbling on to the crash site is just so cool to me

Pacencia from GRA that thing is a killer.

Mine would have to be the 5.56mm pistol, it looks great and its appearance is taken from that of the gun used in the original Blade Runner

Fallout 1 - minigun because I can easily blast the supermutant bastards for killing Dogmeat

Haven't played enough of Fallout 2 to know.

Fallout 3 - Xuanlong assault rifle, just a cool weapon for killing supermutants for killing Dogmeat again (the puppy perk can't bring back my true Dogmeat).

Fallout New Vegas - The All American, a very useful, powerful gun to deal with enemies, does jack shit to Deathclaws though.

Fallout 4 - As you said @Wertologist, they all suck. Modded guns are the ones I use.

Easy, 'Lucky' based on the colt single action army, the greatest handgun ever made, it has six bullets, more than enough to kill anything that moves.

Sure you could argue that the engravings give you no tactical advanatage what so ever (that is unless you plan on selling it) but a 2.5x crit chance, faster rate of fire, lower ap cost and lower spread over the standard 357. magnum revolver makes it a rare exception.

Mine’s a boring choice: All-American from NV, cos of the plentiful ammo, decent scope, decent damage and a counterpart to the Gobi rifle in boone’s hands

FOV: cyberdog gun, he was such a good boi
F03: Sniper rifle it was really easy to take car of enclave with it
F04: If I had to pick one it'd be the combat shotgun

F1: AK-112 assault rifle. Easy to get ammo, and tearing through someone someone is satisfying in a way I don't really experience in other games.

F3: R91. Handsome gun, good sound to it. In a close second place is the N99 10mm pistol, mostly because it also sounds great.

FNV: SMMG from Lonesome Road. Does good damage and, surprise surprise, I think it sounds nice.

Just like Clarke. The R91.

I mean, it's a meaty rifle you can't deny that. Especially with the wooden furniture. I'm a sucker for wooden furniture on firearms. That classic G3 looking style just gets me. I love it. It's stylish.

Right now, for fallout 4 it's the Nuka-Nuke Launcher.

From Fallout 1 and 2 it'll be the combat shotgun(wich one there's a mod in New Vegas for that wepon and i love it)

in Fallout 3 is Vengeance the unique variant of the gatling laser

for Fallout New Vegas is maybe the hunting rifle with his mod kits, the anti-material rifle and the marksman carbine.

i have "Fallout" 4 but i'm not playing that shit until i got a new pc.

Fallout 1 and 2: The .223 pistol for the fact that it's got high stopping power and good armor penetration, while completely looking badass and being a nice nod to Blade Runner.

Fallout 3: Callahan's magnum, yet again a nice nod to pop culture (Dirty Harry) and deals heavier damage than the Blackhawk. I also dig the 10mm SMG for looking cool.

Fallout New Vegas: A tie between That Gun, A Light Shining in Darkness, and Holy Hand Grenades. That Gun references both the OG Fallouts and Blade Runner while being one of my favorite pistols. A Light Shining in Darkness is great solely because I'm a sucker for 1911s. Holy Hand Grenades are great for fighting the Legate while referencing Monty Python.

Fallout 4 I don't own (yet), but I dig the handmade rifles for looking like AKs.

I always liked the Survivalist's Rifle in FNV. The backstory is nice, and the gun is stupid strong.

YK42B pulse rifle, Plasma Caster, Laser Rifle, Vindicator Minigun and the Flamer from Fo1+2.
Anti-Material Rifle, Sniper Rifle, 357 Revolver, Sleepytyme, Hunting Revolver/Ranger Sequoia, Riot Shotgun, Lever Action Shotgun and Holorifle from New Vegas.